Multivariable constrained process control via Lyapunov R-functions Aldo Balestrino a , Andrea Caiti a , Sergio Grammatico a,⋆ , a Department of Energy and Systems Engineering, University of Pisa, Largo Lucio Lazzarino 1, 56122 Pisa, Italy. Abstract This paper proposes a smooth control Lyapunov function with maximal controlled domain of attraction for the state-feedback control of constrained uncertain linear systems describing the dynamics of multivariable processes. Constructive algorithms are shown to build such a control Lyapunov function within a merging procedure due to the so called R-functions. Robustness with respect to polytopic model un- certainties and disturbance rejection are also discussed. The controlled dynamics of two chemical reactions are simulated to show the benefits of the proposed strategy. Key words: Generated Lyapunov functions, Uncertain linear systems, Process control. 1 Introduction Chemical processes are continuously faced with the requirements of becoming safer, more reliable, and more economical in operation. The design of effec- tive chemical process control systems, inherently Multi-Input Multi-Output (MIMO) and nonlinear, needs to be both rigorous and practical [12]. More- over, the unavoidable presence of physical constraints on the process variables and in the capacity of control actuators not only limit the nominal perfor- mance of the controlled system, but can also affect the stability of the overall system. As a consequence, the stabilization of such processes is one of the most attractive research areas for the chemical and control engineering community [11]. ⋆ Corresponding author Sergio Grammatico, e-mail: grammatico.sergio@gmail.com. Preprint submitted to Elsevier 4 June 2012